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A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variablesâ value or values.
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only includes predicates that apply to individual objects, other logics may allow predicates that apply to collections of objects defined by other predicates.
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are sometimes regarded as zero-place predicates. In a sense, these are nullary (i.e. 0-
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238:. For instance, in a standard semantics for first-order logic, the formula
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is a symbol that represents a property or a relation. For instance, in the
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Problems in Set Theory, Mathematical Logic, and the Theory of
Algorithms
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is a predicate that applies to the individual constants
19:"Predicate (logic)" redirects here. For other uses, see
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Symbol representing a property or relation in logic
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21:Predicate (disambiguation) § Logic
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86:is a predicate that applies to the
509:. New York: Springer. p. 52.
445:Free variables and bound variables
391:, predicates are understood to be
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317:stand in the relation denoted by
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234:, predicates are interpreted as
349:Predicates in different systems
219:is exactly a function from the
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2241:History of mathematical logic
2317:Basic concepts in set theory
2166:Primitive recursive function
109:. Similarly, in the formula
277:if the entities denoted by
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1230:SchröderâBernstein theorem
957:Monadic predicate calculus
616:Foundations of mathematics
534:Introduction to predicates
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2263:Philosophy of mathematics
2212:Automated theorem proving
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1337:Von NeumannâBernaysâGödel
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499:Lavrov, Igor Andreevich;
403:from a set element to a
393:characteristic functions
1913:Self-verifying theories
1734:Tarski's axiomatization
685:Tarski's undefinability
680:incompleteness theorems
460:Predicate functor logic
337:. Since predicates are
2312:Propositional calculus
2287:Mathematics portal
1898:Proof of impossibility
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856:Propositional calculus
389:law of excluded middle
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266:{\displaystyle R(a,b)}
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137:{\displaystyle R(a,b)}
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2109:Computably enumerable
2009:Model complete theory
1801:Principia Mathematica
861:Propositional formula
690:BanachâTarski paradox
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59:{\displaystyle P(a)}
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2258:Mathematical object
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2114:Computable function
1908:Reverse mathematics
1834:Logical consequence
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1706:elementary function
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1332:TarskiâGrothendieck
851:Logical connectives
781:Logical equivalence
631:Logical consequence
480:Well-formed formula
416:autoepistemic logic
397:indicator functions
359:propositional logic
339:non-logical symbols
88:individual constant
36:first-order formula
2327:Mathematical logic
2056:Transfer principle
2019:Semantics of logic
2004:Categorical theory
1980:Non-standard model
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621:Information theory
570:Mathematical logic
465:Predicate variable
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601:First-order logic
501:Maksimova, Larisa
440:Classifying topos
374:first-order logic
343:first-order logic
330:{\displaystyle R}
310:{\displaystyle b}
290:{\displaystyle a}
197:{\displaystyle b}
177:{\displaystyle a}
157:{\displaystyle R}
102:{\displaystyle a}
79:{\displaystyle P}
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2231:Category of sets
2124:Decision problem
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1742:Boolean algebras
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724:LöwenheimâSkolem
611:Formal semantics
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2099:Church encoding
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2061:Truth predicate
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1883:Complete theory
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1240:Gödel numbering
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841:Boolean algebra
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791:Equiconsistency
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2014:Satisfiability
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1931:Interpretation
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1010:Ordinal number
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2176:Recursive set
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2022:
2020:
2017:
2015:
2012:
2010:
2007:
2005:
2002:
1998:
1995:
1994:
1993:
1990:
1986:
1985:of arithmetic
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1892:from ZFC
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1791:non-Euclidean
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1668:Example
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1468:
1465:
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1428:
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1425:by definition
1423:
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1325:
1323:
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1313:
1312:KripkeâPlatek
1310:
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1305:
1301:
1298:
1296:
1293:
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1291:
1288:
1287:
1285:
1281:
1273:
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1268:
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1191:
1188:
1187:
1185:
1183:
1179:
1175:
1167:
1164:
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1159:
1157:
1156:constructible
1154:
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1134:
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989:
986:
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968:
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948:
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926:
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869:
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864:
862:
859:
857:
854:
852:
849:
847:
844:
842:
839:
838:
836:
834:
833:Propositional
830:
824:
821:
819:
816:
814:
811:
809:
806:
804:
801:
799:
796:
792:
789:
788:
787:
784:
782:
779:
777:
774:
772:
769:
767:
764:
762:
761:Logical truth
759:
757:
754:
753:
751:
749:
745:
742:
740:
736:
730:
727:
725:
722:
720:
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715:
712:
710:
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705:
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697:
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677:
674:
673:
671:
669:
663:
658:
652:
649:
647:
644:
642:
639:
637:
634:
632:
629:
627:
624:
622:
619:
617:
614:
612:
609:
607:
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602:
599:
597:
594:
590:
587:
586:
585:
582:
581:
579:
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571:
564:
559:
557:
552:
550:
545:
544:
541:
535:
532:
531:
527:
518:
512:
508:
507:
502:
495:
492:
485:
481:
478:
476:
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468:
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453:
451:
448:
446:
443:
441:
438:
437:
433:
428:
424:
421:
417:
413:
410:
406:
402:
398:
394:
390:
386:
382:
379:
375:
371:
369:) predicates.
368:
364:
360:
356:
355:
354:
348:
346:
344:
340:
324:
304:
284:
276:
257:
254:
251:
245:
237:
233:
228:
226:
222:
218:
214:
210:
209:Gottlob Frege
207:According to
205:
191:
171:
151:
144:, the symbol
128:
125:
122:
116:
96:
89:
73:
66:, the symbol
50:
44:
37:
33:
29:
22:
2278:
2076:Ultraproduct
1923:Model theory
1888:Independence
1824:Formal proof
1816:Proof theory
1799:
1772:
1729:real numbers
1701:second-order
1612:Substitution
1530:
1489:Metalanguage
1430:conservative
1403:Axiom schema
1347:Constructive
1317:MorseâKelley
1283:Set theories
1262:Aleph number
1255:inaccessible
1161:Grothendieck
1045:intersection
951:
932:Higher-order
920:Second-order
866:Truth tables
823:Venn diagram
606:Formal proof
505:
494:
419:
352:
229:
225:truth values
220:
216:
212:
206:
31:
25:
2322:Fuzzy logic
2186:Type theory
2134:undecidable
2066:Truth value
1953:equivalence
1632:non-logical
1245:Enumeration
1235:Isomorphism
1182:cardinality
1166:Von Neumann
1131:Ultrafilter
1096:Uncountable
1030:equivalence
947:Quantifiers
937:Fixed-point
906:First-order
786:Consistency
771:Proposition
748:Traditional
719:Lindström's
709:Compactness
651:Type theory
596:Cardinality
475:Truth value
470:Truthbearer
427:fuzzy logic
405:truth value
2301:Categories
1997:elementary
1690:arithmetic
1558:Quantifier
1536:functional
1408:Expression
1126:Transitive
1070:identities
1055:complement
988:hereditary
971:Set theory
516:0306477122
486:References
385:set theory
2268:Supertask
2171:Recursion
2129:decidable
1963:saturated
1941:of models
1864:deductive
1859:axiomatic
1779:Hilbert's
1766:Euclidean
1747:canonical
1670:axiomatic
1602:Signature
1531:Predicate
1420:Extension
1342:Ackermann
1267:Operation
1146:Universal
1136:Recursive
1111:Singleton
1106:Inhabited
1091:Countable
1081:Types of
1065:power set
1035:partition
952:Predicate
898:Predicate
813:Syllogism
803:Soundness
776:Inference
766:Tautology
668:paradoxes
401:functions
387:with the
236:relations
217:predicate
32:predicate
2253:Logicism
2246:timeline
2222:Concrete
2081:Validity
2051:T-schema
2044:Kripke's
2039:Tarski's
2034:semantic
2024:Strength
1973:submodel
1968:spectrum
1936:function
1784:Tarski's
1773:Elements
1760:geometry
1716:Robinson
1637:variable
1622:function
1595:spectrum
1585:Sentence
1541:variable
1484:Language
1437:Relation
1398:Automata
1388:Alphabet
1372:language
1226:-jection
1204:codomain
1190:Function
1151:Universe
1121:Infinite
1025:Relation
808:Validity
798:Argument
696:theorem,
503:(2003).
434:See also
2195:Related
1992:Diagram
1890: (
1869:Hilbert
1854:Systems
1849:Theorem
1727:of the
1672:systems
1452:Formula
1447:Grammar
1363: (
1307:General
1020:Forcing
1005:Element
925:Monadic
700:paradox
641:Theorem
577:General
420:unknown
399:(i.e.,
395:or set
230:In the
213:meaning
1958:finite
1721:Skolem
1674:
1649:Theory
1617:Symbol
1607:String
1590:atomic
1467:ground
1462:closed
1457:atomic
1413:ground
1376:syntax
1272:binary
1199:domain
1116:Finite
881:finite
739:Logics
698:
646:Theory
513:
221:domain
211:, the
1948:Model
1696:Peano
1553:Proof
1393:Arity
1322:Naive
1209:image
1141:Fuzzy
1101:Empty
1050:union
995:Class
636:Model
626:Lemma
584:Axiom
378:terms
367:arity
215:of a
28:logic
2071:Type
1874:list
1678:list
1655:list
1644:Term
1578:rank
1472:open
1366:list
1178:Maps
1083:sets
942:Free
912:list
662:list
589:list
511:ISBN
297:and
184:and
30:, a
1758:of
1740:of
1688:of
1220:Sur
1194:Map
1001:Ur-
983:Set
425:In
414:In
407:).
383:In
372:In
357:In
204:.
26:In
2303::
2144:NP
1768::
1762::
1692::
1369:),
1224:Bi
1216:In
361:,
2224:/
2139:P
1894:)
1680:)
1676:(
1573:â
1568:!
1563:â
1524:=
1519:â
1514:â
1509:â§
1504:âš
1499:ÂŹ
1222:/
1218:/
1192:/
1003:)
999:(
886:â
876:3
664:)
562:e
555:t
548:v
519:.
380:.
325:R
305:b
285:a
261:)
258:b
255:,
252:a
249:(
246:R
192:b
172:a
152:R
132:)
129:b
126:,
123:a
120:(
117:R
97:a
74:P
54:)
51:a
48:(
45:P
23:.
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